Hyper-parameter tuning of physics-informed neural networks: Application to Helmholtz problems
This work addresses the challenge of tuning PINNs for researchers in computational physics, though it is incremental as it applies an existing optimization technique to a specific domain.
The paper tackled the problem of optimizing hyper-parameters in physics-informed neural networks (PINNs) for solving forward physical problems, specifically applying a Gaussian process-based Bayesian optimization method to the Helmholtz equation in bounded domains, with results including performance studies and comparisons to finite element methods in 2D and 3D.
We consider physics-informed neural networks (PINNs) [Raissi et al., J.~Comput. Phys. 278 (2019) 686-707] for forward physical problems. In order to find optimal PINNs configuration, we introduce a hyper-parameter optimization (HPO) procedure via Gaussian processes-based Bayesian optimization. We apply the HPO to Helmholtz equation for bounded domains and conduct a thorough study, focusing on: (i) performance, (ii) the collocation points density $r$ and (iii) the frequency $κ$, confirming the applicability and necessity of the method. Numerical experiments are performed in two and three dimensions, including comparison to finite element methods.